document.write( "Question 182132This question is from textbook college algebra
\n" ); document.write( ": the problem is radical 3+2n + radical 2-2n =3, when i type radical it means the
\n" ); document.write( "3+2n and 2-2n are under the radical sign. i hope you can help me understand. \n" ); document.write( "

Algebra.Com's Answer #136776 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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the problem is radical 3+2n + radical 2-2n = 3,
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\n" ); document.write( " $\"sqrt%283%2B2n%29\"$ + $\"sqrt%282-2n%29\"$ = 3
\n" ); document.write( ":
\n" ); document.write( " $\"sqrt%283%2B2n%29\"$ = 3 - $\"sqrt%282-2n%29\"$
\n" ); document.write( "square both sides:
\n" ); document.write( "3 + 2n = (3 - $\"sqrt%282-2n%29\"$ )^2
\n" ); document.write( "FOIL the right side
\n" ); document.write( "3 + 2n = 9 - 6 $\"sqrt%282-2n%29\"$ + (2-2n)
\n" ); document.write( ":
\n" ); document.write( "3 + 2n = 9 + 2 - $\"6sqrt%282-2n%29\"$ - 2n
\n" ); document.write( ":
\n" ); document.write( "3 + 2n = 11 - $\"6sqrt%282-2n%29\"$ - 2n
\n" ); document.write( ":
\n" ); document.write( "3 - 11 + 2n + 2n = - $\"6sqrt%282-2n%29\"$
\n" ); document.write( ":
\n" ); document.write( "4n - 8 = - $\"6sqrt%282-2n%29\"$
\n" ); document.write( ":
\n" ); document.write( "square both sides, FOIL the left side
\n" ); document.write( "16n^2 - 64n + 64 = 36(2-2n)
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\n" ); document.write( "16n^2 - 64n + 64 = 72 - 72n
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\n" ); document.write( "16n^2 - 64n + 72n + 64 - 72 = 0
\n" ); document.write( ":
\n" ); document.write( "16n^2 + 8n - 8 = 0
\n" ); document.write( "Simplify, divide by 8
\n" ); document.write( "2n^2 + n - 1 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(2n - 1)(n + 1) = 0
\n" ); document.write( "Two solutions:
\n" ); document.write( "n = $\"1%2F2\"$
\n" ); document.write( "n = -1
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\n" ); document.write( "Check both solution in original equation:
\n" ); document.write( "n = .5
\n" ); document.write( " $\"sqrt%283%2B2%28.5%29%29\"$ + $\"sqrt%282-2%28.5%29%29\"$ = 3
\n" ); document.write( " $\"sqrt%283%2B1%29\"$ + $\"sqrt%282-1%29\"$ = 3
\n" ); document.write( " $\"sqrt%284%29\"$ + $\"sqrt%281%29\"$ = 3; a good solution
\n" ); document.write( ":
\n" ); document.write( "n = -1
\n" ); document.write( " $\"sqrt%283-2%29\"$ + $\"sqrt%282-%28-2%29%29\"$ = 3
\n" ); document.write( " $\"sqrt%281%29\"$ + $\"sqrt%284%29\"$ = 3; also a good solution
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